Regenerative actuation in motion control

ABSTRACT

A motion controlled system for a robotic system stores energy when the robotic system uses negative power and releases the stored energy when the robotic system uses positive power. The motion controlled system calculates the power for causing the robotic system to follow a prescribed motion and applies the appropriate control signals to the robotic system in response to detected parameters of the robotic system.

RELATED APPLICATIONS

This application claims the benefit of and priority from U.S.provisional application No. 60/689,502 which is incorporated byreference herein in its entirety.

This application is related to U.S. patent application Ser. No.11/402,487 filed on Apr. 11, 2006; U.S. patent application Ser. No.11/395,654, filed on Mar. 30, 2006; U.S. patent application Ser. No.11/038,978 filed on Jan. 19, 2005; U.S. patent application Ser. No.11/038,692 filed on Jan. 19, 2005; U.S. patent application Ser. No.11/038,691 filed on Jan. 19, 2005; U.S. patent application Ser. No.10/151,647 filed on May 16, 2002; U.S. provisional application No.60/301,891 filed on Jun. 29, 2001; No. 60/353,378 filed on Jan. 31,2002; and No. 60/670,732 filed on Apr. 12, 2005, the contents of all areincorporated by reference herein in their entirety.

FIELD OF THE INVENTION

The present invention relates to motion control, and more particularlyto motion control with regenerative actuation.

BACKGROUND OF THE INVENTION

Locomotion of robotic or bio-robotic systems such as humanoid robots orexoskeletons typically involves periods of energy generation and energyabsorption at each body segment. The generated energy is associated withpositive work and is typically produced from actuation, external forces,and/or the natural dynamics of the system. The absorbed energy isassociated with negative work, or the energy that is to be dissipated byantagonist actuation, external forces, or through passive structures inthe system. In humans, the energy absorption phase, typically associatedwith deceleration of the limbs is achieved through a combination ofantagonist muscle activation and the passive elements in the muscles andother supporting structures in the joint. In robotic systems, such ashumanoids, the energy is sometimes absorbed through motor clutches,passive structures in the system, or by reverse actuation. In reverseactuation, the motors generate torque that opposes the angular velocityof the segment. However, generating torque that opposes the angularvelocity of the segment is highly inefficient in terms of powerconsumption.

What is needed is a system and method for providing more efficient powerconsumption for robotic and bio-robotic systems.

SUMMARY OF THE INVENTION

A method for controlling a motion controlled system includes computingpower for executing a motion that may or may not be predetermined;generating a first control signed to apply energy to the motioncontrolled system if the computed power is above a first predeterminedlevel; generating a second control signal to draw energy from the motioncontrolled system if the computed power is below a second predeterminedlevel; and generating a third control signal to store the energy drawnfrom the motion controlled system. The motion controlled system may be arobotic joint.

The features and advantages described in the specification are not allinclusive and, in particular, many additional features and advantageswill be apparent to one of ordinary skill in the art in view of thedrawings, specification, and claims. Moreover, it should be noted thatthe language used in the specification has been principally selected forreadability and instructional purposes, and may not have been selectedto delineate or circumscribe the inventive subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram illustrating a motion controlled system forcontrolling a robotic/bio-robotic system according to one embodiment ofthe present invention.

FIG. 2 is a diagram illustrating a free body diagram of human lowerextremity for one side of the body with forces and moments actingthereon.

FIG. 3 is a timing diagram of ankle joint power generated or absorbedduring one cycle of gait.

FIG. 4 is a timing diagram of knee joint power generated or absorbedduring one cycle of gait.

FIG. 5 is a timing diagram of hip joint power generated or absorbedduring one cycle of gait.

FIG. 6 is a block diagram of a robot that includes an inverted pendulumcontrolled by a pair of actuators according to the present invention.

FIG. 7 is a free body diagram illustrating of a single body with forcesand moments acting thereon.

FIG. 8 is a flowchart illustrating one embodiment of a methodology forcontrolling power to and from the robot of FIG. 1 according to thepresent invention.

DETAILED DESCRIPTION

A preferred embodiment of the present invention is now described withreference to the figures where like reference numbers indicate identicalor functionally similar elements. Also in the figures, the left mostdigits of each reference number corresponds to the figure in which thereference number is first used.

Reference in the specification to “one embodiment” or to “an embodiment”means that a particular feature, structure, or characteristic describedin connection with the embodiments is included in at least oneembodiment of the invention. The appearances of the phrase “in oneembodiment” in various places in the specification are not necessarilyall referring to the same embodiment.

The system and method provides a motion controlled system for a roboticsystem that stores energy when the robotic system uses negative powerand that releases the stored energy when the robotic system usespositive power. The motion controlled system calculates the power forcausing the robotic system to follow a prescribed motion and applies theappropriate control signals to the robotic system in response todetected parameters of the robotic system.

For a robotic system for human locomotion, the system absorbs and storesenergy in an ankle and decelerates when a heel strikes the ground. Asthe gait continues, the system releases the stored energy.

1 System

FIG. 1 is a block diagram illustrating a motion controlled system 100for controlling a robotic/bio-robotic system according to one embodimentof the present invention. The motion controlled system 100 comprises acontroller 102, a robot 104, and a summer 106. The robot 104 may be, forexample, a humanoid robot, or a wearable human exoskeleton system. Therobot 104 includes actuators for controlling the motion of the robot inresponse to control signals from the controller 102. The controller 102generates the control signals based on a desired motion and feedback,such as position and angular velocity, from the robot 104. Thecontroller 102 may be a processor of any known type.

In one embodiment, the robot 104 is an orthosis controlled by anactuator, such as an Ankle Foot Orthosis. The initial step in thecontrol process of the controller 102 may be to generate the desiredtrajectory of the robot 104. One embodiment of the present inventionprovides several methods for computing a trajectory in multi-dimensionalspace that describes the desired motion of the robot 104. A trajectorydescribed in joint space can be specified by the vector q, anddetermines the motion of each degree of freedom, its velocity, and itsacceleration. Alternatively, a trajectory can be described in task spaceby a set of Cartesian variables which are related to joint varibles q.For example, depending on the application, the desired motion of thesystem can be planned off-line, or generated at run-time using a varietyof trajectory generation schemes. In another embodiment, the userspecifies only the desired goal position and orientation of a point onthe robot, and the controller 102 determines the exact shape of the pathto get there, the duration, the velocity profile, and other details.

Many types of controllers 102 can be designed to achieve the desiredmotion. For example, an inverse dynamics based tracking controller canbe used to generate the control commands that when applied to the robot,will reproduce the desired motion. For example, the controller 102 maybe one of those described in the related patent applications cited aboveand incorporated herein by reference.

The control objective may not necessarily be trajectory tracking. Otherperformance criteria such as stability, balance, energy minimization,etc. may also be used when designing the controller 102. In general, thefunction of the controller 102 is to produce the control action(typically specified as a force or torque) that will generate a motionsatisfying a specified performance criterion. The control action istransformed to a quantity that is accepted as input by the actuators ofthe robot 104, such position commands, current, or voltage.

As an overview, controlled motion of any physical system (or load)involves periods of energy generation as well as energy absorption.Energy is generated in order for a physical system to do positive workwhile energy is absorbed if the work is negative. Energy can be put intoa system in different ways. For example, externally powered actuators orexternal forces may deliver energy to a system. Energy may also be addedas a result of the system's natural dynamics. For example, gravitationalforces can convert potential energy into kinetic energy, therebyproducing energy. Like energy generation, energy may also be absorbed indifferent ways. In motion control, a typical way to absorb (ordissipate) energy is through externally powered antagonistic (orreverse) actuation. Energy may also be dissipated by an external force.In one embodiment, energy is absorbed through passive structures, suchas springs and dampers.

During periods of energy generation or absorption, actuators in mostphysical systems use supply power, regardless of the direction in thepower flow. In principal, there is no need to supply power to theactuators during the energy absorption phase if, for example, theabsorbed energy can be precisely controlled and dissipated passively.Furthermore, the dissipated energy can be potentially stored and laterrecovered by a regenerative mechanism. The ability to identify thegeneration or absorption phase during the operation of the system,coupled with an approach to passively control and regenerate theabsorbed energy can significantly reduced the power requirements inmotion controlled systems.

Although, energy regeneration in hybrid-electric vehicles is an examplewhere energy is recovered when a load is decelerated, that technologycurrently does not involve the motion control problem considered here.In particular, the control action to decelerate the vehicle is not basedon tracking a prescribed motion profile. Rather, an integral part of thecontroller is a human in-the-loop which provides the necessary feedbackto decelerate the vehicle. Furthermore, the bandwidth of the control inhybrid-electric vehicles is much different from the majority ofapplications using motion control. The system 100 of the presentinvention is described for the control of single, or multi-link rigidbody mechanical systems, such as industrial robots, humanoid robots, orwearable human exoskeletons. However, the principles of regenerativeactuation and control of the system 100 apply to control of any physicalsystem.

The energetics of motion controlled systems are described herein throughpower analysis. A systematic procedure identifies the energy absorptionphase and the energy generation phase of the system 100 that iscontrolled to follow a prescribed motion. Based on these criteria, ahybrid actuator system may be designed and integrated into the robot 104of the motion controlled system whereby the actuation mechanism providesactive control, or passive control and regeneration, depending on thedirection of the power flow. One example is an actuator/controlmechanism to regeneratively control a single link inverted pendulum byusing spring based actuation as described below in conjunction with FIG.6. Spring based actuation concepts have the advantage that springs comein a variety of shapes and sizes and are available in large quantities.An actuator constructed upon the properties of a spring is intrinsicallycompliant and can dissipate energy. Furthermore, the use of a spring aspart of the actuator allows the use of stored energy. One of the firstrealizations of a compliant actuator was the MIT Series ElasticActuator. See, for example, G. A. Pratt and W. M. Williamson, “Serieselastic actuators”, IEEE Int'l Conf. on Intelligent Robots and Systems,pages 399-406 (1995), the contents of which are incorporated herein intheir entirety. However, the spring stiffness in the Series ElasticActuator could not be modulated. A spring actuator that can adjust itsstiffness will have a resonance behavior over a range of frequencies. Inorder for an actuator to passively control the force or torque, avariable compliance actuator is used. One such actuator is described inJ. W. Hurst, J. E. Chestnut, and A. A. Rizzi, “An actuator withphysically variable stiffness for highly dynamic legged locomotion”,IEEE Int'l Conf. on Robotics and Automation, pages 4662-4667, NewOrleans, La., (2004), the contents of which are incorporated herein intheir entirety.

2 Energetic Studies of Human Locomotion

The mechanical energies are excellent means of quantifying anddescribing the efficiencies associated with the controller 102. Theinstantaneous power calculation at each joint reveals whether energy isabsorbed or generated. If the computed power at a given joint ispositive, then the actuators are doing positive work and energy isdelivered to the segment. If joint power is negative, then energy isabsorbed by the system. The controller 102 controls the delivery ofpower to the segment and the absorption of the energy by the system.

In order to illustrate the positive and negative power flows, theenergetics of human motion during gait are considered. Human motionanalysis is compelling because the body segment parameters, as well askinesiological measurements such as ground reaction forces and motioncapture are readily available, providing the necessary inputs todetermine joint torques and joint powers. Furthermore, human motionanalysis provides insight about the bandwidth requirements inapplications involving humanoid robots, or wearable human exoskeletonsystems.

FIG. 2 is a diagram illustrating a free body of human lower extremityfor one side of the body with forces and moments acting thereon. FIG. 7is a free body diagram illustrating of a single body with forces andmoments acting thereon. The free body of FIG. 2 may be analyzed assingle bodies such as shown in FIG. 2.

For the sake of clarity, the pelvis, thigh, shank and foot are shownspaced apart, but these parts are coupled at joints C₂, C₃ and C₄. Thebody segments are enumerated starting with the pelvis (B₁) and workingoutward to the foot (B₄) and the B_(i) pointing to the center of mass ofthe body segment. The body segments have a mass m_(i). The groundreaction force and moment, denoted by Γ_(gr) and N_(gr) respectively,correspond to the reaction loads acting at the distal end of the lastsegment in the chain, for example, the foot. The point of application ofthe ground reaction force is the center of pressure (cop).

To determine the joint powers at the ankle, knee, and hip, standard gaitmeasurements including motion capture and force plate data were obtainedfrom the Gait CD. See, for example, C. L. Vaughan, B. Davis, and J.O'Connor. Dynamics of Human Gait, Kiboho Publishers, Cape Town SouthAfrica, 2nd edition (1999), the contents of which are incorporatedherein in their entirety. The gait data obtained from the Gait CDcontained 15 lower extremity marker data based on the Helen Hayes markerset, anthropometric measurements such as limb-dimensions and body bass,and force plate data under two feet. The marker and anthropometric datawere used to calculate the body segment parameters and joint centersbased on the statistical regression equations provided by Vaughan et al,noted above. The marker data were filtered using a second orderButterworth low-pass filter with a cut-off frequency of 6 HZ. The forceplate data was filtered at 50 HZ. The sampling frequency of the markerdata was 60 HZ. The Euler angles and center of gravity of each bodysegment were calculated in order to determine the generalizedcoordinates (or configuration) of each segment.

At a particular joint, the inner product of the joint moments (denotedby N) and the joint angular velocities, (denoted by W) are then used todetermine the joint powers. The power P is calculated as follows:P=N ^(T) W  (1)

FIG. 3 is a timing diagram of ankle joint power generated or absorbedduring one cycle of gait. FIG. 4 is a timing diagram of knee joint powergenerated or absorbed during one cycle of gait. FIG. 5 is a timingdiagram of hip joint power generated or absorbed during one cycle ofgait.

A kinematics and inverse dynamics procedure, as described in U.S. PatentApplication Publication US2005/0209535, filed as U.S. patent applicationSer. No. 11/038,692, the contents of which are incorporated herein intheir entirety, may be used to calculate, respectively, the angularvelocity W and joint moments N at the ankle, knee, and hip. Theassociated joint powers can be calculated from Equation 1. The resultsare illustrated in FIGS. 3-5, which clearly illustrate that in humangait, the muscles generate and absorb energy during the entire gaitcycle. Each period of energy generation and absorption can be very short(a fraction of a second); therefore, control with large bandwidths areessential by the muscle actuators. Consider, for example, the anklepower plot. At heel strike (which occurs at t=0.25 sec), the ankle jointpower absorbs energy to decelerate the limb for about 0.5 seconds.During this phase, the muscle actuators at the ankle are doing negativework. The ankle is doing negative work approximately 50% of the time.

3 Inverted Pendulum Model

FIG. 6 is a diagram illustrating a regenerative actuation and motioncontrolled system 600 including a simple planar inverted pendulumaccording to one embodiment of the present invention. A more complexmulti-link system, such as the system of FIG. 2, can be viewed as aseries of coupled inverted pendulums stacked on top of each other. See,for example, B. Dariush and K. Fujimura, “Fuzzy logic based controlmodel of human postural dynamics”, SAE Conference on Digital HumanModeling for Design and Engineering, Detroit, Mich. (2000), the contentsof which are incorporated herein in their entirety. (See also U.S. Pat.No. 6,633,783, the contents of which are incorporated herein in theirentirety.).

The regenerative actuation and motion controlled system 600 comprises apendulum 602 that is constrained on a base 603 at a pivot point 604 andfurther comprises actuators 606-1 and 606-2 that generate respectiveforces F₁ and F₂ which rotate the pendulum 602 clockwise orcounterclockwise, respectively. Suppose the forces F₁ and F₂ correspondto two separate actuator forces that are actively or passivelygenerated. In one embodiment, a single actuator 606 generates the forcesF₁ and F₂. For simplicity, and without loss of generality, assume theline of action of the forces F₁ and F₂ is along the circumference of acircle centered at the joint pivot 604 and of radius d, which representsthe moment arm of the two forces. In one embodiment, the actuators 606comprise cable and pulley systems. In humans, the analogy can be made tothe control of a sagittal arm by a flexor/extensor muscle pair. See, forexample, J. A. Dinneen and H. Hemami, “Stability and movement of aone-link neuro-musculo-skeletal sagittal arm”, IEEE Transactions onBiomedical Engineering, 40(6):541-548 (1993), the contents of which areincorporated herein in their entirety. Analogous to human muscles thatproduce a force under contraction of muscle fibers, in one embodiment,the actuators 606 produce a positive force under compression.

The physical parameters of the system 600 are the mass m of the pendulum602, considered to be concentrated at a distance k from the axis (pivot604) of the joint, and the moment of inertia I. The angle θ is measuredfrom the vertical and is positive in the clockwise direction.

The effective length and incremental length of the actuators 606-1 and606-2 that generate the respective forces F₁ and F₂ as a function of θare given by Equations (2) and (3):

$\begin{matrix}{L = {L_{o} + {\frac{\partial L^{T}}{\partial\theta}( {\theta - \theta_{o}} )}}} & (2) \\{{dL} = {\frac{\partial L^{T}}{\partial\Theta}d\;\theta}} & (3)\end{matrix}$where L=[L₁ L₂]^(T) correspond to the vector form of lengths in theactuators 606-1 and 606-2, respectively, L_(o) is the 2×1 vectorcorresponding to the initial length of the actuators 606, and θ_(o) isangle at the initial length. The term ∂L^(T)/∂Θ represents the momentarm matrix and is given by Equation (4):

$\begin{matrix}{\frac{\partial L^{T}}{\partial\Theta} = \begin{bmatrix}d & {- d}\end{bmatrix}} & (4)\end{matrix}$

The relationship between the joint torque and the actuator forces isgiven by Equation (5):

$\begin{matrix}{\tau = {{{- \frac{\partial L^{T}}{\partial\Theta}}F} = {d( {F_{2} - F_{1}} )}}} & (5) \\{where} & \; \\{F = \begin{bmatrix}F_{1} & F_{2}\end{bmatrix}^{T}} & (6)\end{matrix}$

Note the convention is used that positive torque is in the clockwisedirection. The dynamic equations of motion for this system are describedby:I{umlaut over (θ)}−mkg sin(θ)=τ  (7)where g is the gravitational acceleration constant. A model based methodto control the inverted pendulum 602 to track a desired trajectory θ_(d)is given by,τ=I{umlaut over (θ)}*−mkg sin(θ)  (8)where {umlaut over (θ)}* is given by,{umlaut over (θ)}*={umlaut over (θ)}_(d) +K _(d)({dot over (θ)}_(d)−{dotover (θ)})+K _(p)(θ_(d)−θ)  (9)The terms K_(p) and K_(d) are positive definite position and derivativefeedback gains, respectively.

In an alternative embodiment to the model based control approach, themotion of the pendulum 602 can be controlled using one of many differentcontrol laws, such as a proportional-integral-derivative (PID)controller given by Equation (10):τ=K _(p)(θ_(d)−θ)+K _(I)∫(θ_(d)−θ)dt+K _(d)({dot over (θ)}_(d)−{dot over(θ)})  (10)where K_(I) is the integral feedback gain. The tracking performance ofthe control law in Equation 10 may be inferior to that of Equation 8;however, Equation 8 is robust to modeling errors and parameteruncertainties.

The control laws in Equations 8 and 10 compute the actuator torque forexecuting a desired motion profile. The actuator 606 most widely used inrobotic applications is the permanent magnet DC motor. Such motors aredriven by a controllable voltage or current source. Most motormanufacturers allow the user to indirectly command a desired torque byapplying a voltage that is proportional to the armature current. Becausemotor torque is proportional to armature current, the torque can bedirectly and accurately controlled.

FIG. 8 is a flowchart illustrating one embodiment of a methodology forcontrolling power to and from the robot 104 of FIG. 1 or the actuators606 of FIG. 6 according to the present invention.

The controller 102 distributes torque to the linear actuators 606 toproduce forces F₁ and F₂ while satisfying the torque relation given byEquation 5 and by applying the appropriate control signals to theactuators 606. The controller 102 distributes torque using a policy thatdepends on the direction of the instantaneous joint power. Thecontroller 102 passively controls the joint when the system is absorbingenergy and actively controls the joint when the system is generatingenergy. This principle can be applied to any joint by first computingthe joint power and then determining the mode of the actuator as agenerator or a motor.

The controller 102 obtains 802 or determines the desired motion of thejoint, and determines 804 (from sensors or by prediction) the angular orlinear velocity at the joint. The controller 102 determines 806 ageneralized torque or force to cause the joint to move in accordancewith the desired motion, and computes 808 the power of the joint. If thecomputed power is positive 810, the controller 102 provides controlsignals to cause the actuators 406 to generate 512 the correspondingenergy for rotating the joint, and actively controls 814 the joint. Onthe other hand, the joint power is negative 810, the joint absorbs 816energy, and the controller 102 commands the actuators to store 818energy and passively controls the joint.

The control of the actuator as shown in FIG. 8 is next described for arotational joint.

For a rotational joint, the quantities used to determine the power Pgenerated by an actuator is the product of net joint torque τ, and thejoint angular velocity, ω={dot over (θ)}, as described in Equation (11):P=τω  (11)

Based on the direction of the instantaneous power flow, the forces F₁and F₂ have an active component which use supply power and a passivecomponent which stores energy and later releases the stored energy.

If the instantaneous power is negative 810 (P<0), the system can becontrolled by dissipating 818 energy passively. Under this scenario,suppose the actuators 606 store the dissipated energy by using passiveforces F_(1p) and F_(2p). This may be achieved with an actuator 606 withspring-like properties according to Hooke's law,F _(1p(store)) =k _(s1) δt ₁  (12)F _(2p(store)) =k _(s2) δt ₂  (13)

where k_(s1) and k_(s2) are tunable spring coefficient and δt1 and δl₂represents the displacement of the spring. Since this system isredundantly actuated (2 actuators control 1 joint), the distribution ofstored energy in the two passive actuators is not unique. The actuatormechanism provides the passive forces in each spring that does notoppose the direction of the calculated torque to execute the desiredmotion. In other words, the stored energy should be a byproduct ofresistive torques, which are used to dissipate energy with the samemagnitude and direction of the control torque. Controlling the magnitudeof the stored force (and therefore joint torque) may be achieved byusing an actuator with an adjustable spring constant. An example of aspring actuator with adjustable stiffness was developed by Hurst et al.See, for example, J. W. Hurst, J. E. Chestnut, and A. A. Rizzi, “Anactuator with mechanically adjustable series compliance”, CarnegieMellon University Technical Report: CMU-RI-TR-04-24, Pittsburgh, Pa.(2004), the contents of which are incorporated herein in their entirety.See also, for example, Hurst et al. “An actuator with physicallyvariable stiffness for highly dynamic legged locomotion” noted above.Alternatively, several springs can be combined in parallel and recruitedat different times in order to control the force. The stored energy isreleased when the system goes into energy generation phase 812.

If the instantaneous power is positive 810 (P>0), the system can becontrolled by delivering 814 active power by either forces F₁ or F₂,depending on the direction of the torque. Let F_(1a) and F_(2a) be theactive component of the forces generated by the two actuators 606. Thejoint torque can be expressed as,τ=d(F _(1a) +F _(p(release))) if τ≦0  (14)τ=d(F _(2a) +F _(p(release))) if τ≧0  (15)

where F_(p (release))) is the force that is released from one or both ofthe passive springs, depending on the current state. The released springforce of each actuator 606 is in the same direction as the active forcecomponent. The active component of actuator force F₁ is computed asfollows,

$\begin{matrix}{F_{1\; a} = \{ \begin{matrix}{{{- \tau}/d} - F_{p{({release})}}} & {{{if}\mspace{14mu}\tau} \leq 0} \\{0} & {otherwise}\end{matrix} } & (16)\end{matrix}$

where τ is obtained by the control law in Equation 8 or Equation 10. Theactive component of actuator force F₂ is computed by,

$\begin{matrix}{F_{2a} = \{ \begin{matrix}{{{- \tau}/d} - F_{p{({release})}}} & {{{if}\mspace{14mu}\tau} \leq 0} \\{0} & {otherwise}\end{matrix} } & (17)\end{matrix}$

Another embodiment of the present invention provides energyregeneration, which uses actuators 606 as motors when energy needs to begenerated by the system 812 and uses them as generators when energyneeds to be absorbed/regenerated by the system 816. According to afurther embodiment, absorbed/regenerated energy can be stored 818 andused to provide active actuation 814 when the actuators are used asmotors.

4 Multi-Link Systems

The equations of motion of an n degree of freedom, unconstrained,multi-link rigid body system, such as shown in FIG. 2, can be describedby the following differential equation,M(q){umlaut over (q)}+h(q,{dot over (q)})=T  (18)where vector q is an n×1 vector of generalized coordinates that describethe configuration of the system, M is an n×n joint space inertia matrix,and h is an n×1 vector describing the effects of the coriolis,centrifugal, gravitational, and friction forces. The vector T is n×1 andrepresents the generalized forces (or torques). The multi-link versionof the tracking controller 102 in Equation 8 is given by,T=M(q){umlaut over (q)}*+h(q,{dot over (q)})  (19)where{umlaut over (q)}*={umlaut over (q)} _(d) +K _(d)({dot over (q)} _(d)−{dot over (q)})+K _(p)(q _(d) −q)  (21)

where q_(d) is an n×1 vector of the desired generalized coordinates, andthe feedback gains K_(d) and K_(p) are n×n positive definite, diagonalmatrices. Without loss of generality, the system is assumed to have i=1. . . n rotational joints and each joint is actuated. The control lawfor the i_(th) actuator is denoted by T_(i).

The PID control law in Equation 10 is an independent joint controller.Therefore, with modification of the variable names, the multi-linkversion of the controller is identical to the single link controlpresented in Equation 10.T _(i) =K _(pi)(q _(di) −q _(i))+K _(Ii)∫(q _(di) −q _(i))dt+K _(di)(q_(di) −q _(i))  (22)where the feedback gains are all scalars, as in Equation 10. If T_(i)actuates the i_(th) joint in this system, and w_(i) is the associatedangular velocity of the i_(th) joint, then the power to actuate thejoint is given by,P _(i) =T _(i) w _(i)  (23)

The initial step in the control process is to generate the desiredtrajectory. There are several methods for computing the trajectory inmulti-dimensional space which describes the desired motion of a robot. Atrajectory described in joint space can be specified by the vector q,and determines the motion of each degree of freedom, its velocity, andits acceleration. Alternatively, a trajectory can be described in taskspace by a set of Cartesian variables which are related to jointvaribles q. Depending on the application, the desired motion of thesystem can be planned off-line, or generated at run-time using a varietyof trajectory generation schemes. It is sometimes sufficient that theuser specify only the desired goal position and orientation of a pointon the robot, and leave the system to decide on the exact shape of thepath to get there, the duration, the velocity profile, and otherdetails.

While particular embodiments and applications of the present inventionhave been illustrated and described herein, it is to be understood thatthe invention is not limited to the precise construction and componentsdisclosed herein and that various modifications, changes, and variationsmay be made in the arrangement, operation, and details of the methodsand apparatuses of the present invention without departing from thespirit and scope of the invention as it is defined in the appendedclaims.

1. A method for controlling a motion controlled system, the methodcomprising: generating, using the controller, a trajectory specifying adesired motion of the motion controlled system to a desired position forthe motion controlled system in joint space or in task space; computingpower to be applied to the motion controlled system to produce a motionmoving the motion controlled system to a first position along thetrajectory; generating, using the controller, a first control signal tosupply energy to the motion controlled system to move the motioncontrolled system along the trajectory when the computed power is abovea first predetermined level; generating, using the controller, a secondcontrol signal to draw energy from the motion controlled system as movesthe motion controlled system along the trajectory when the computedpower is below a second predetermined level; and generating, using thecontroller, a third control signal to store the regenerated energy. 2.The method of claim 1 wherein the motion controlled system is a roboticjoint.
 3. The method of claim 1 further comprising: generating, usingthe controller, a fourth control signal to supply the stored energy tothe motion controlled system when the computed power is above the firstpredetermined level, wherein the generating, using the controller, thefirst control signal includes generating the first control signal tosupply stored energy to the motion controlled system.
 4. The method ofclaim 1 further comprising: measuring angular velocity of the motioncontrolled system, wherein the computing power to be supplied to themotion controlled system includes: determining the torque to be appliedto the motion controlled system in response to the measured angularvelocity, and computing the power to be supplied to the motioncontrolled system based on the computed torque.
 5. The method of claim 4wherein the determining the torque includes computing the torque to beapplied to the motion controlled system in response to the measuredangular velocity.
 6. The method of claim 4 wherein determining thetorque includes measuring the torque to be applied to the motioncontrolled system in response to the measured angular velocity.
 7. Themethod of claim 1 further comprising: detecting motion of the motioncontrolled system, wherein computing power to be applied to the motioncontrolled system further includes computing power to be applied to themotion controlled system based on the detected motion and the motionmoving the motion controlled system to a first position along thetrajectory.
 8. The method of claim 1 wherein the motion controlledsystem includes an actuator that brakes the motion controlled system. 9.The method of claim 8 wherein the actuator includes a regeneration mode.10. The method of claim 1 wherein the motion controlled system includesan actuator system comprising first and second actuators, the first andsecond actuators cause the motion controlled system to move in first andsecond directions, respectively, the first actuator using positive powerin the first direction and storing or releasing energy in the seconddirection, the second actuator using positive power in the seconddirection and storing or releasing energy in the first direction.
 11. Asystem comprising: a motion controlled system for controlling motion ofa structure in response to first, second and third control signals; acontroller for generating a trajectory specifying a desired motion ofthe motion controlled system to a desired position for the motioncontrolled system in joint space or in task space, computing power to beapplied to the motion controlled system to generate a motion moving themotion controlled system to a first position along the trajectory, forgenerating the first control signal to supply energy to move the motioncontrolled system along the trajectory when the computed power is abovea first predetermined level, for generating the second control signal todraw energy from the motion controlled system as the motion controlledsystem moves along the trajectory when the computed power is below asecond predetermined level; and for generation the third control signalto store the energy drawn from the motion controlled system.
 12. Thesystem of claim 11 wherein the motion controlled system includes arobotic joint.
 13. The system of claim 11 wherein the controller furthergenerates the fourth control signal to supply the stored energy to themotion controlled system when the computed power is above the firstpredetermined level, and generating the first control signal includesgenerating the first control signal to supply stored energy to themotion controlled system.
 14. The system of claim 11 wherein the motioncontrolled system measures angular velocity of the structure, whereinthe controller computes power to be applied to the motion controlledsystem by determining the torque to be applied to the motion controlledsystem in response to the measured angular velocity, and computing thepower to be applied to the motion controlled system based on thecomputed torque.
 15. The system of claim 11 wherein the motioncontrolled system further detects motion of the structure, wherein thecontroller computes power to be applied to the motion controlled systembased on the detected motion and the motion moving the motion controlledsystem to a first position along the trajectory.
 16. The system of claim11 wherein the motion controlled system includes an actuator that brakesthe motion controlled system.
 17. The system of claim 16 wherein theactuator includes a regeneration mode.
 18. The system of claim 11wherein the motion controlled system includes an actuator systemcomprising first and second actuators, the first and second actuatorscause the motion controlled system to move in first and seconddirections, respectively, the first actuator using positive power in thefirst direction and storing or releasing energy in the second direction,the second actuator using positive power in the second direction andstoring or releasing energy in the first direction.
 19. The system ofclaim 11 wherein the motion controlled system includes a movable member,and includes an actuator system for moving the member in first andsecond directions, the actuator system comprises first and secondactuators, the first and second actuators provide a positive force inresponse to a compression thereof in response to movement in the firstand second directions, respectively, of the movable member, and providea negative force in response to an expansion thereof in response tomovement in the second and first directions, respectively, of themovable member.
 20. The system of claim 11 wherein the motion controlledsystem includes a base, a movable member coupled to the base androtatable about an axis, and includes an actuator system for rotatingthe moveable member in first and second directions about the axis, theactuator system comprises first and second actuators, each first andsecond actuators including a first end coupled to the base and includinga second end coupled to the movable member, the second ends of the firstand second actuators being coupled to opposite sides of the movablemember.
 21. The system of claim 20 wherein, the first and secondactuators provide a positive force in response to a compression thereofin response to movement in the first and second directions,respectively, of the movable member, and provide a negative force inresponse to an expansion thereof in response to movement in the secondand first directions, respectively, of the movable member.